Multiplying symbol streams by rectangular matrix of (P/M)×1 vectors

ABSTRACT

Closed loop multiple-antenna wireless communications system with antenna weights determined by maximizing a composite channel signal-to-interference-plus-noise ratio minimum. Multiplexed symbol streams over subsets of antennas enhance throughput.

This application is a Divisional of application Ser. No. 10/301,392,filed Nov. 21, 2002 now U.S. Pat. No. 7,181,167.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority from U.S. provisional patentapplication Nos. 60/331,718, filed Nov. 21, 2001, 60/339,704, filed Dec.13, 2001, and 60/343,424, filed Dec. 20, 2001.

BACKGROUND OF THE INVENTION

The present invention relates to wireless digital communications, andmore particularly to space diversity transmission systems and methods.

Wireless communication systems include a large variety of approaches,such as frequency division multiple access (FDMA), time divisionmultiple access (TDMA), code division multiple access (CDMA), andcombinations. FDMA uses separate frequency bands for duplexcommunication; whereas, TDMA partitions a single frequency band intotime slots which as allocated to one or the other end of a communicationlink. CDMA uses a spread spectrum approach.

Spread spectrum wireless communications utilize a radio frequencybandwidth greater than the minimum bandwidth required for thetransmitted data rate, but many users may simultaneously occupy thebandwidth. Each of the users has a pseudo-random code for “spreading”information to encode it and for “despreading” (by correlation) receivedspread spectrum signals and recovery of information. Such multipleaccess typically appears under the name of code division multiple access(CDMA). The pseudo-random code may be an orthogonal (Walsh) code, apseudo-noise (PN) code, a Gold code, or combinations (modulo-2additions) of such codes. After despreading the received signal at thecorrect time instant, the user recovers the corresponding informationwhile other users' interfering signals appear noise-like. For example,the interim standard IS-95 for such CDMA communications employs channelsof 1.25 MHz bandwidth and a pseudo-random code pulse (chip) intervalT_(C) of 0.8138 microsecond with a transmitted symbol (bit) lasting 64chips. The recent 3GPP wideband CDMA (WCDMA) proposal employs a 3.84 MHzbandwidth and the CDMA code length applied to each information symbolmay vary from 4 chips to 256 chips. Indeed, UMTS (universal mobiletelecommunications system) approach UTRA (UMTS terrestrial radio access)provides a spread spectrum cellular air interface with both FDD(frequency division duplex) and TDD (time division duplex) modes ofoperation. UTRA currently employs 10 ms duration frames partitioned into15 time slots with each time slot consisting of 2560 chips (T_(C)=0.26microsecond).

The air interface leads to multipath reception, so a RAKE receiver hasindividual demodulators (fingers) tracking separate paths and combinesthe finger results to improve signal-to-noise ratio (SNR). The combiningmay use a method such as the maximal ratio combining (MRC) in which theindividual detected signals in the fingers are synchronized and weightedaccording to their signal strengths or SNRs and summed to provide thedecoding. That is a RAKE receiver typically has a number of DLL or TDLcode tracking loops together with control circuitry for assigningtracking units to the strongest received paths. Also, an antenna arraycould be used for directionality by phasing the combined signals fromthe antennas.

Further, UTRA allows for transmit diversity, both open-loop andclosed-loop (receiver feedback). The open-loop transmit diversityincludes both time-switched transmit diversity (TSTD) and space-timeblock-coding-based transmit diversity (STTD). Closed loop techniquesprovide some significant gain over open-loop transmit diversitytechniques by using channel state information (CSI) at the transmitter.For FDD the CSI can be made available at the transmitter via a feedbackchannel; whereas, for TDD the channel can be directly measured at thetransmitter by exploiting the reciprocity (uplink and downlink using thesame channel).

The current closed-loop transmit diversity transmits only one datastream via all the transmit antennas, hence achieves the maximumdiversity gain. However, for a given modulation scheme, its peak datarate is limited. Another possible transmission scheme is to transmit thesame number of data streams as the number of transmit antennas. Whileachieving maximum peak data rate (termed multiplexing gain), thediversity gain of such scheme is limited by the number of receiveantennas, especially when the number of receive antennas is the same asthe number of transmit antennas (which is typically the case). Forinstance, when linear detection is used at the receiver, the diversitygain for each stream is Q−P+1, where Q and P are the number of receiveand transmit antennas, respectively. Hence, it is sometimes desirable touse a transmission scheme that combines transmit diversity and datamultiplexing.

SUMMARY OF THE INVENTION

The present invention provides multiplexed multi-antenna transmitdiversity adapted to a composite channel of physical channel plusequalization and/or interference cancellation.

This has the advantages including increased performance for wirelesscommunications.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings are heuristic for clarity.

FIGS. 1 a-1 b are flow diagrams.

FIGS. 2 a-2 d illustrate transmitters.

FIGS. 3 a-3 c show receivers.

FIGS. 4-5 present simulation results.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 1. Overview

The preferred embodiment methods determine antenna weightings inclosed-loop multi-antenna multiplexed-data-stream systems byincorporating the effect of multipath interference as well as thedetection scheme used at the receiver for closed-loop transmit diversityweight vector selection. An example of such selection criterion is tomaximize minimum signal-to-interference-plus-noise ratio (SINR) of thecomposite channel (physical channel plus equalization/interferencecancellation), where SINR is defined as the ratio between the averagepower of the desired signal component and the average power ofinterference plus noise.

Preferred embodiment transmissions and reception use such antennaweightings with adaptive updating and may include multi-inputmulti-output (MIMO) systems; see FIGS. 1 a-1 b flow diagrams. Thesemethods apply to the various wireless communications approaches (CDMA,TDMA, etc.). and extend to multiplexed data stream versions. For a TDDsystem the transmitter is also a receiver over the same physical channeland thus can directly estimate the channel; whereas, in an FDD systemthe receiver must provide channel state information to the transmitter.

The determination of antenna weightings derives from optimization ofSINR of the composite channel, and thus depends upon the detectionmethod. The detection can be by any convenient method such as maximumlikelihood, linear zero-forcing, iterative zero-forcing, linear minimummean square error, iterative minimum mean square error, and so forth.

For a FDD system the receiver must signal the transmitter. Thus with anFDD CDMA cellular system having mobiles with multiple antennas theantenna weighting signaling with be both uplink and downlink.

Preferred embodiment communications systems use preferred embodimentencoding and decoding methods. FIGS. 2 a-2 c illustrate preferredembodiment transmitter functional blocks, and FIGS. 3 a-3 b showpreferred embodiment receiver functional blocks.

In preferred embodiment cellular wireless communications systems basestations and mobile users could each include one or more digital signalprocessors (DSPs) and/or other programmable devices with stored programsfor performance of the signal processing of the preferred embodimentmethods. Alternatively, specialized circuitry could be used. The basestations and mobile users may also contain analog integrated circuitsfor amplification of inputs to or outputs from antennas and conversionbetween analog and digital; and these analog and processor circuits maybe integrated as a system on a chip (SoC). The stored programs may, forexample, be in ROM or flash EEPROM integrated with the processor orexternal. The antennas may be parts of receivers with multiple fingerRAKE detectors for each user's signals. Exemplary DSP cores could be inthe TMS320C6xxx or TMS320C5xxx families from Texas Instruments.

2. TDMA-Based Single Stream Preferred Embodiments

The single-stream preferred embodiments consider transmission of asingle stream of symbols, . . . , s(n), s(n+1), s(n+2), . . . , from Pantennas (P≧2) with antenna weights w₁, w₂, . . . , w_(P) and receptionby Q antennas (Q≧1) with maximal ratio combining (MRC) of multipathsfollowed by various detection methods. Each detection method leads to aspecific method for determination of transmission antenna weightings.

For comparison purposes, first look at the simple case with negligibleintersymbol interference. Presume that the channel from P transmitantennas (FIG. 2 d) to Q receiver antennas (FIG. 3 c) has at most Lresolvable paths (L-tap delay line channel model) and that the Q×Pchannel matrix H_(j) of attenuations and phase shifts corresponds to thejth delay line tap. With negligible intersymbol interference and amaximal ratio combining (MRC) receiver, the P antenna weightings w₁, w₂,. . . , w_(P) applied to the symbol stream for transmission over the Pantennas are taken to maximize the reception:w=argmax_(uεS) u ^(H)(Σ_(1≦j≦L) H _(j) ^(H) H _(j))uwhere S denotes the set of all allowable weighting vectors, and udenotes a P-vector of antenna weightings u₁, u₂, . . . , u_(P) in S. Forexample, S could be the set of P-vectors u with complex components and∥u∥=1; in this case, w equals the eigenvector of the P×P matrix(Σ_(1≦j≦L)H_(j) ^(H) H_(j)) having the maximum eigenvalue. Whereas, S isa finite set of complex P-vectors with unit norm for FDD CDMA.

In contrast, the first preferred embodiments presume equalization in thereceiver and use channel state information (CSI) for the compositechannel (physical channel plus equalizer) to determine the P antennaweightings. FIGS. 2 a, 3 a show a transmitter and receiver for a systemwith preferred embodiment antenna weighting determinations which adaptto the channel conditions; the “delay” function in the receiver allowstime for the transmitter to adjust to antenna weightings as determinedby the receiver and signalled to the transmitter. The (q,p)th element ofH_(j) is the channel from the pth transmit antenna to the qth receiveantenna for the jth delay or multipath. Let . . . , s(n), s(n+1),s(n+2), . . . denote the stream of transmitted symbols.

First, for a TDMA system the received baseband discrete-time signal(sampled at the symbol rate, extension to sampling at sub-symbol rate isstraightforward) is:

${r(n)} = {\begin{bmatrix}{r_{1}(n)} \\{r_{2}(n)} \\\cdots \\{r_{Q}(n)}\end{bmatrix} = {{\sum\limits_{0 \leq j \leq {L - 1}}{H_{j}w\mspace{11mu}{s\left( {n - j} \right)}}} + {{noise}\mspace{11mu}(n)}}}$where w is the P-vector of weights used at the transmitter and the Ltaps are relabeled 0≦j≦L−1 to coincide with the corresponding delay.(Code-division differs from the foregoing time-division in thatdespreading in code-division allows direct tracking of multipaths andreplacement of the tapped delay line of time-division with a receiverhaving multiple tracking units.)

Collect a sequence of N received samples to form one detection window:

$r = {\begin{bmatrix}{r(0)} \\{r(1)} \\\cdots \\{r\left( {N - 1} \right)}\end{bmatrix} = {{{H\left( {I_{N} \otimes w} \right)}s} + {noise}}}$where

$H = \begin{bmatrix}H_{0} & 0 & 0 & \cdots & 0 & 0 & \cdots & 0 \\H_{1} & H_{0} & 0 & \cdots & 0 & 0 & \cdots & 0 \\H_{2} & H_{1} & H_{0} & \cdots & 0 & 0 & \cdots & 0 \\\vdots & \vdots & \vdots & ⋰ & \vdots & \vdots & \; & \vdots \\H_{L - 1} & H_{L - 2} & H_{L - 3} & \cdots & H_{0} & 0 & \cdots & 0 \\0 & H_{L - 1} & H_{L - 2} & \cdots & H_{1} & H_{0} & \cdots & 0 \\\vdots & \vdots & \vdots & \; & \; & \; & ⋰ & \; \\0 & 0 & 0 & \cdots & H_{N - L} & H_{N - L - 1} & \cdots & H_{0}\end{bmatrix}$ ${I_{N} \otimes w} = \begin{bmatrix}w & 0 & 0 & \cdots & 0 \\0 & w & 0 & \cdots & 0 \\0 & 0 & w & \cdots & 0 \\\cdots & \; & \; & ⋰ & \; \\0 & 0 & 0 & \cdots & w\end{bmatrix}$Thus r is an NQ-vector, H is an NQ×NP block Toeplitz channel matrix,(I_(N){circle around (x)}w) is an NP×N matrix, and s is the N-vector oftransmitted symbols of the detection window: s(0), s(1), . . . , s(N−1).N is presumed larger than L so the lower left N−L triangle of H is allQ×P 0s. Indeed, practical systems may use values such as N=16 or 32 andL=6 Also, presume within a detection window the channel stateinformation (CSI) is constant (not updated) and thus also the weights ware constant within the detection window.

Application of a matched filter (including maximal ratio combining ofthe tap delays) yields the N×1 output y:y=(I _(N) {circle around (x)}w ^(H))H ^(H) rMore explicitly, (for n<N−L):

$\begin{matrix}{{y(n)} = {{w^{H}H_{0}^{H}{r(n)}} + {w^{H}H_{1}^{H}{r\left( {n + 1} \right)}} + \ldots + {w^{H}H_{L - 1}^{H}{r\left( {n + L - 1} \right)}}}} \\{= {w^{H}\left\{ {\sum\limits_{0 \leq j \leq {L - 1}}{H_{j}^{H}{r\left( {n + j} \right)}}} \right\}}}\end{matrix}$Then in terms of the block of transmitted symbols, s, the output is:

$\begin{matrix}{y = {\left( {I_{N} \otimes w^{H}} \right){H^{H}\left\lbrack {{{H\left( {I_{N} \otimes w} \right)}s} + {noise}} \right\rbrack}}} \\{= {{\left( {I_{N} \otimes w^{H}} \right)H^{H}{H\left( {I_{N} \otimes w} \right)}s} + {\left( {I_{N} \otimes w^{H}} \right)H^{H}{noise}}}}\end{matrix}$

Next, we consider various detection methods. Different types ofdetection methods can be used at the receiver, such as the simplemaximum ratio combining (MRC) receiver above. However, this type ofreceiver is not resistant to multipath interference. Some examples ofinterference-resistant detection method include the optimal maximumlikelihood detection, linear detection (zero forcing or minimum meansquare error), and iterative detection (zero forcing or minimum meansquare error). The details of each detection method are given below.

The weight vector w is selected based on a criterion that takes intoaccount the effect of multipath interference. There are a number ofpossible criteria that can be used, including the Rake-based criterionmentioned in Section 1 (which does not fully account for the effect ofmultipath interference). An example criterion that includes the effectof multipath interference is to select w such that the off-diagonalelements of matrix (I_(N){circle around (x)}w^(H)) H^(H) H (I_(N){circlearound (x)}w) are minimized in some sense (e.g. minimize the sum ofoff-diagonal terms, minimize the off-diagonal term with maximummagnitude). Notice that this criterion does not depend on the receivertype. Different types of receiver, however, respond differently tomultipath interference. Hence, intuitively, the selection criteria thattake into account the receiver type (detection method) result in betterperformance. Such receiver-specific selection criteria will be discussedin the following paragraphs.

In general, the optimal maximum likelihood detection would estimate thetransmitted symbols s by ŝ which is the vector of symbols that minimizesthe sum of the errors in the received signal on the receiver antennas.That is,ŝ=argmin_(s) ∥r−H(I _(N) {circle around (x)}w)s∥ ²where the minimization is taken over the set of possible transmittedsymbol vectors which depends on the symbol mapping. The weight vector(w) selection at the receiver can be performed based on symbol errorrate (SER) for maximum likelihood detection (which reflects bit errorrate or frame error rate of the system). It can be shown that an upperbound of SER is (assuming noise variance is unity)

${SER} \leq {\sum\limits_{z \in \Delta}{\kappa_{z}{Q\left( \sqrt{{{{H\left( {I_{N} \otimes w} \right)}z}}^{2}/2} \right)}}}$where Δ={(u−v): u,vεS, u≠v}, S is the set of all possible transmittedsymbol vectors, κ_(z) is the multiplicity of z in S, and Q(.) is theGaussian Q-function. This upper bound can be used for selecting w:choose w that minimizes the SER upper bound. But such a maximumlikelihood detection becomes computationally intensive with largerantenna systems. Both linear and iterative detectors are based on theidea of interference suppression/-cancellation. Possible methods includezero forcing (ZF) and minimum mean square error (MMSE). In thefollowing, the linear MMSE (LMMSE) and iterative MMSE (IMMSE) detectorsare explained. A zero-forcing-based detectors (LZF and IZF) can beobtained from MMSE analogs by removing the identity term in the matrixinverse.

Generally, for linear detection use a linear equalizer which transformsthe matched filter N-vector window output y into N-vector statistic z=Fywhich will estimate transmitted N-vector of symbols s. The N×N matrix Fdetermines the SINR(n) for symbol s(n) in the window, and the minimumSINR(n) determines the overall system error rate (either BER or FER).Consequently, the preferred embodiment methods determine the antennaweightings w to maximize the minimum SINR(n). That is, given equalizerF, pick w so thatw=argmin_(uεS)min_(1≦n≦N) SINR(n)where u denotes a P-vector of antenna weightings in the set of allowedweightings S. The dependence of SINR(n) on F and antenna weightings fordifferent detectors is as follows.

For linear zero-forcing (LZF) detection, the N×N equalizer matrix F isfound as the inverse of the channel model:F=[G^(H)G]⁻¹where the NQ×N antenna-weighted channel time-window matrix G is givenby:G=H(I _(N) {circle around (x)}w)so G^(H)G is N×N Hermitian and invertible (a 0 eigenvalue corresponds toeither 0 antenna weights, which means no transmission, or a 0 channel,which means no reception). And then SINR(n) is given by:SINR(n)_(LZF) =ρ/[G ^(H) G] ⁻¹ _(n,n)where ρ is the normalized power per symbol and [G^(H)G]⁻¹ _(n,n) denotesthe row n, column n element of the matrix [G^(H)G]⁻¹. Thus the SINRs forthe symbols are proportional to the reciprocals of the diagonal elementsof the equalizer matrix.

Similarly for linear minimum mean square error (LMMSE) detection theequalizer matrix F is picked so the mean square error (MSE), E[∥Fy−s∥²], is minimized. The (theoretically derived) linear transformationF is given by:F=[ρ ⁻¹ I _(N) +G ^(H) G] ⁻¹And the resultant SINR(n) is:SINR(n)_(LMMSE)=ρ/[ρ⁻¹ I _(N) +G ^(H) G] ⁻¹ _(n,n)−1And for these two linear detectors the preferred embodiment antennaweightings w are computed to maximize the minimum composite channelSINR; namely,w _(LZF) =argmin_(uεS)min_(1≦n≦N)1/[(I _(N) {circle around (x)}u ^(H))H^(H) H(I _(N) {circle around (x)}u)]⁻¹ _(n,n)w _(LMMSE) =argmin_(uεS)min_(1≦n≦N)1/[I _(N)+ρ(I _(N) {circle around(x)}u ^(H))H ^(H) H(I _(N) {circle around (x)}u)]⁻¹ _(n,n)−1And when the channel coefficients, H, are updated, the antennaweightings, w. can updated for both transmission and reception. Forexample, in a TDMA cellular telephone system the updating may occurevery 0.5-ms.

For nonlinear detection, such as iterative (decision-feedback)equalizers, more computations are required than for the correspondinglinear detector. The iterative equalizer is implemented in N steps witheach step making a decision on one of the N symbols in the window. Eachstep includes a linear transformation (ZF or MMSE) followed by a harddecision-feedback (across space and time). That is, a resulting linearlytransformed statistic z=Fy is essentially a soft estimate of a componentof s.

The SINR for iterative equalizers (IZF or IMMSE) can be computed as forthe linear equalizers. Of course, the optimization to determine theantenna weightings w has higher complexity. The IMMSE detector is asequence of N linear MMSE detection stages, where each detection outputsboth a hard and a soft estimate of one of the N symbols in the detectionblock. The hard estimate is used to regenerate the interference from theso-far estimated symbols which is then subtracted from the receivedsignal, and the difference used for the next linear symbol estimation.More explicitly, presume the symbols are to be estimated in numericalorder and let ŝ_(k) denote the hard estimate of the kth symbol s_(k) andlet the N-vector ŝ^((k)) denote the vector with components 1, 2, . . . ,k equal to ŝ₁, ŝ₂, . . . , ŝ_(k), respectively, and with the remainingN−k components all equal to 0. The iteration's nth step will outputŝ^((n)) from an initialization of ŝ⁽⁰⁾=0. The nth step (nth lineardetector) proceeds as follows:

-   -   (a) Regenerate the interference created by previously-estimated        symbols s₁, . . . , s_(n−1) using the channel matrix; that is,        form G ŝ^((n−1)). Note that only the first n−1 rows of blocks of        G are used because the last N−n+1 components of ŝ^((n−1)) equal        0, so a simpler matrix with rows of blocks n, n+1, . . . N all        0s could be used.    -   (b) Subtract the regenerated interference of substep (a) from        the received signal to have an interference-cancelled signal:        r−G ŝ^((n−1)).    -   (c) Apply the linear equalizer filter F to the matched-filtered        (N×NQ matrix G^(H)) interference-cancelled signal from        substep (b) to generate a soft output z^((n)) which estimates        the yet-to-be-estimated symbols s_(n), s_(n+1), . . . , s_(N).        Because the interference cancellation (decision feedback) likely        is not perfect, further suppress the interfering symbols by use        of a modified linear equalizer filter F^((n)) which derives from        the portion of the channel matrix from sources (antennas) n,        n+1, . . . , N. That is, z^((n))=F^((n)) G^(H) [r−G ŝ^((n−1))]        where the matrix F^((n)) ignores the portion of the channel        relating to the previously-estimated symbols (and analogously G        restricted to already estimated symbols and G^(H) restricted to        ignore these channels). The particular form of F^((n)) depends        upon the linear detector type and on assumption about the        decision feedback error. In effect, the channel matrix is        partitioned into two parts with the part relating to the        previously-estimated symbols used to generate the interference        estimate plus interference-cancelled signal and with the part        relating to the yet-to-be-estimated symbols used for detection        of the interference-cancelled signal.    -   (d) Make a hard decision on the pth component of the soft        estimate z^((n)) to generate the hard estimate ŝ_(p) and update        the hard estimate vector ŝ^((n)).        In particular, for assumed error-free decision feedback and IZF        detection:

${F^{(n)}G^{H}} = \begin{bmatrix}0_{{({n - 1})} \times Q} \\{\left\lbrack {A_{n}^{H}A_{n}} \right\rbrack^{- 1}A_{n}^{H}}\end{bmatrix}$where A_(k) is the NQ×(N−n+1) matrix of the last N−n+1 columns of blocksof G; that is, A_(n)=[g_(n) g_(n+1) . . . g_(N)] with g_(k) the kthcolumn (NQ×1) of the NQ×N channel matrix G. Of course, g_(k) is thechannel of the kth symbol from the weighted P antennas to the receivedNQ-vector. Then the SINR(n) is given by:SINR(n)=ρ/[A _(n) ^(H) A _(n)]⁻¹ _(1,1)SINR(n)=ρ/[A _(n) ^(H) A _(n)]⁻¹ _(1,1)And the antenna weightings follows as before from maximizing the minimumSINR(n).

Analogously for IMMSE in which

${F^{(n)}G^{H}} = \begin{bmatrix}0_{{({n - 1})} \times Q} \\{\left\lbrack {{A_{n}^{H}A_{n}} + {\rho^{- 1}I_{N - n + 1}}} \right\rbrack^{- 1}A_{n}^{H}}\end{bmatrix}$and the resulting SINR can be written asSINR(n)=ρ/[A _(n) ^(H) A _(n)+ρ⁻¹ I _(N−n+1)]⁻¹ _(1,1)−1

Ordered iterative detection based on the symbol post-detection SINR isoften used to reduce the effect of decision feedback error. Let thedetection order be π(1), π(2), . . . , π(N) where π( ) is a permutationof the N integers {1, 2, . . . , N}; that is, the first estimated symbol(hard estimate output of the first step of the iteration) will beŝ_(π(1)) and the corresponding nonzero element of ŝ⁽¹⁾. The maximum SINRof the components of the first soft estimate z⁽¹⁾, which estimates all Psymbols, determines π(1). Similarly, the SINRs of the components ofz⁽²⁾, which estimates all of the symbols except s_(π(1)), determinesπ(2), and so forth. The partitioning of the channel matrix at each stepis analogous.

Note that the soft estimates z₁, z₂, . . . , z_(N) for the transmittedblock of symbols s₁, s₂, . . . , s_(N) (i.e., the output z^((n)) _(π(n))from the nth step) are used in a sequence decoder, such as a Viterbidecoder or a Turbo decoder, in the form of log likelihood ratios (LLRs).

Other detection schemes are also possible. For example, a receiverconsisting of a channel equalizer (to equalize H instead of G) followedby coherent combining with (I_(N){circle around (x)}w) can be used. Inthis case, the operation can be described as follows:z=(I _(N) {circle around (x)}w ^(H))Frwhere F=[ρ⁻¹I_(NQ)+H^(H)H]⁻¹ (LMMSE equalizer) or F=[H^(H)H]⁻¹ (LZFequalizer, which requires Q≧P). In this case, channel equalization isperformed to remove the effect of multipath (frequency selectivity).Then, coherent combining with the weight vector is performed insymbol-by-symbol basis. Closed-form expressions of SINR can also bederived from the definition. In practice, such channel equalizer can beimplemented as an adaptive filter. Note that this scheme is inferior tothe previous equalization scheme as this scheme does not exploit theknowledge of w in equalization. Utilizing w in the previous schemeenables signal space (P-fold) dimensionality reduction.

3. CDMA-Based Single Stream Preferred Embodiments

A CDMA system can have multiple mobile users for the same downlinktransmissions from a base station; the uplink channels for differentmobiles users are generally different, but for downlink the usersexperiences a common channel. For the general case of K users aftercollecting samples of the received signal at the chip rate, the basebandreceived signal NN_(C)Q-vector (where N_(C) is the CDMA spreadingfactor) can be written as:

$\begin{matrix}{r = {{\sum\limits_{1 \leq k \leq K}{\left. \sqrt{}P_{k} \right.{H_{k}\left( {C_{k} \otimes I_{P}} \right)}\left( {I_{N} \otimes w_{k}} \right)s_{k}}} + {noise}}} \\{= \left\lbrack {{\left. \sqrt{}P_{1} \right.{H_{1}\left( {C_{1} \otimes I_{P}} \right)}\left( {I_{N} \otimes w_{1}} \right)},{\left. \sqrt{}P_{2} \right.{H_{2}\left( {C_{2} \otimes I_{P}} \right)}\left( {I_{N} \otimes w_{2}} \right)},\ldots\mspace{11mu},} \right.} \\{{\left. {\left. \sqrt{}P_{K} \right.{H_{K}\left( {C_{K} \otimes I_{P}} \right)}\left( {I_{N} \otimes w_{K}} \right)} \right\rbrack\begin{bmatrix}s_{1} \\s_{2} \\\vdots \\s_{K}\end{bmatrix}} + {noise}}\end{matrix}$where K is the number of users, P_(k) is the power of the kth user, N isthe symbol block size, H_(k) is the NN_(C)Q×NN_(C)P channel matrix ofthe kth user, C_(k) is the NN_(C)×N CDMA spreading code matrix of thekth user, w_(k) is the weight vector of user k, and s_(k) is a block ofsymbols of user k. In this case multiuser interference cancellation(also known as multiuser detection) is needed. Similar to equalization,linear or iterative interference cancellation (ZF or MMSE) can be usedand the SINR can be computed in the same manner as for the time-divisioncase by considering the total multiuser channel matrixH_(tot)=[√P₁H₁(C₁{circle around (x)}I_(P))(I_(N){circle around (x)}w₁),√P₂H₂(C₂{circle around (x)}I_(P))(I_(N){circle around (x)}w₂), . . . ,√P_(K)H_(K)(C_(K){circle around (x)}I_(P))(I_(N){circle around(x)}w_(k))] so H_(tot) is an NN_(C)×NK matrix for a Q-antenna receiver.For example, the linear ZF and MMSE multiuser interference cancellationfor CDMA arez=[z₁ ^(T)z₂ ^(T) . . . z_(K) ^(T)]^(T)=FrF=[H _(tot) ^(H) H _(tot)]⁻¹ H _(tot) ^(H)(LZF), andF=[H _(tot) ^(H) H _(tot)+ρ⁻¹ I _(NKP)]⁻¹ H _(tot) ^(H)(LMMSE)The SINR for each symbol from each CDMA user can also be defined in thesame manner as that for TDMA. Similarly, iterative detectors for CDMAare analogous to that for CDMA. In practice, linear multiuserinterference cancellation can be implemented in successive or parallelarchitecture.

For downlink applications where the H_(k) are all the same (H_(k)=H) butw_(k) is user-specific (multiple users) interference cancellationdescribed above is a good alternative. Another possible receiver schemefor user k consists of a channel equalizer (which linearly equalizesonly the channel H), the kth user despreader (multiplication with C_(k)^(H){circle around (x)}I_(P)), and symbol-by-symbol coherent combiningwith the weight vector (multiplication with (I_(N){circle around(x)}w_(k) ^(H))). Again, the SINR expression for each symbol from user kcan be derived from SINR definition. In this downlink scenario, theweighting vectors for all of the users can be jointly selected at thebase station maximizing the minimum SINR across all users and symbols(similar to the previous preferred embodiments for equalizers). Thisensures that all of the users experience good performance.

For the downlink applications where both the H_(k) and the w_(k) arecommon (one user with multiple codes: H_(k)=H, w_(k)=w), the aboveinterference cancellation and equalization techniques are applicable. Inthis single-user multi-code downlink scenario, another receiver schemecan be derived by using the following identity:H(C _(k) {circle around (x)}I _(P))(I _(N) {circle around (x)}w)=H(I_(NNc) {circle around (x)}w)C _(k) =H _(eff) C _(k)The new receiver consists of an equalizer for the effective channelH_(eff)=H(I_(NNc){circle around (x)}w) followed by a despreader for userk (multiplication with C_(k) ^(H)). For weight vector selection, onlyone weighting vector needs to be determined, and maximizing the minimumSINR criteria again is used.

For TDMA- and CDMA-based systems, other types of equalizers and/orinterference cancellers can be designed for mitigating the effect ofmultipath interference when closed-loop transmit diversity is used. Foreach type of multipath interference-resistant receiver, an expression ofSINR as a function of the channel realization, spreading code matrices(for CDMA), and weight vectors can be derived and used for preferredembodiment weight vector selection.

4. Multiplexed Streams Preferred Embodiments

The multiplexed stream preferred embodiments combine transmit diversityand multiple data streams to achieve higher data rates. FIGS. 2 b-2 cillustrate transmitters and FIG. 3 b shows a receiver. One data streamcoming from the the symbol mapper is split into M streams. As with theforegoing preferred embodiments, the multiplexed stream preferredembodiment methods determine the antenna weightings from compositechannel characteristics.

In more detail, FIG. 2 b illustrates a generic preferred embodimenttransmitter with M=P/2 units with each unit having two antennas andtransmitting one data stream. Each w_(m) is a 2×1 weighting vectorcorresponding to the mth data stream; and the preferred embodimentmethods provide composite channel determination of the w_(m)s.

More generally, each unit could have K antennas and thus M=P/K. Thenumber of transmit antennas P must be a multiple of K. Of course, thisscheme can be further generalized by accommodating the possibility ofeach unit having different number of antennas. That is, group n isassigned to K_(n) antennas, where K₁+K₂+ . . . +K_(M)=P, where1≦K_(m)<P, M≧2, and P>2. For simplicity, we assume that all the unitshave the same number of antennas for the rest of this description(extension to the most general case is obvious for one skilled in theart).

FIG. 2 c illustrates preferred embodiments with a P×M lineartransformation (weighting matrix) of the M data streams onto the Pantennas. Thus the FIG. 2 c transmitter is a special case with weightingmatrix V given by:

$V = \begin{bmatrix}w_{1} & 0 & \ldots & 0 \\0 & w_{2} & \ldots & 0 \\\vdots & \vdots & ⋰ & \vdots \\0 & 0 & \ldots & w_{M}\end{bmatrix}$

For systems with P transmit antennas the peak data rate is the sum ofpeak data rates of all of the streams. When all of the data streamsshare the same modulation-coding scheme, the peak data rate is simply Mtimes the peak data rate dictated by the modulation-coding scheme.

Consider the P-antenna transmitter and Q-antenna receiver system ofFIGS. 2 c, 3 b. Denote the data (symbol) streams s₁, s₂, . . . , s_(M)by the M-vector s, and denote the Q×P channel by H. For simplicity,assume that the channel is frequency non-selective (single-tap),although extensions to multipath scenarios follow as analogs of thesingle-stream preferred embodiment systems described above. Then thereceived Q-vector signal can be written as:r=HVs+noisewhere the noise is Q-vector AWGN. The Q×M matrix HV is the effectiveMIMO channel matrix, which includes spatial interference among thesymbol streams. To generate sufficient statistics for detection, performmaximal ratio combining (MRC) matched filtering as with thesingle-stream preferred embodiments:y=V^(H)H^(H)r=V^(H) H ^(H)(HVs+noise)Again, various detection methods may be applied; namely, maximumlikelihood, zero-forcing (both linear and iterative), and minimum meansquare error (both linear and iterative). The maximum likelihooddetection solves the following optimization problem:ŝ=argmin_(s) ∥r−HVs∥ ²where the minimization is taken over the set of possible transmittedsymbol vectors which depends on the symbol mapping. The linear detectionmethods apply a linear transformation F to the received y to yield thesoft estimation statistic z=F y by choice of F for ZF and MMSE as:F_(LZF)=[V^(H)H^(H)HV]⁻¹F _(LMMSE) =[V ^(H) H ^(H) HV+I _(M)/ρ]⁻¹where ρ is the average symbol power in the sense that E[ss^(H)]=ρI_(M).

Iterative detectors are constructed from a series of lineartransformations followed by decision-feedback interference cancellation;as described in previous preferred embodiments. Again, the cancellationcan be ordered according to criteria such as largest SINR.

The multipath channel aspect is treated as in the previous preferredembodiments. In this case, the SINR metric must incorporate the effectof multipath interference.

The preferred embodiment weighting vectors/matrix determination againminimizes the symbol error rate (SER) for maximum likelihood detection,and maximizes the minimum SINR for linear and iterative detections;although other criteria could be used. And the resultant weightingvectors/matrix found by the receiver can be signaled to the transmitterin the feedback channel for an FDD system but may, optionally, bedirectly determined by the transmitter for a TDD system. Analogous tothe single-stream embodiment, the following SER upperbound can be used:

${SER} \leq {\sum\limits_{z \in \Delta}{\kappa_{z}{Q\left( \sqrt{{{HV}_{z}}^{2}/2} \right)}}}$where Δ={(u−v): u, vεS, u≠v}, S is the set of all possible transmittedsymbol vectors, κ_(z) is the multiplicity of z in S, and Q(.) is theGaussian Q-function. This upper bound can be used for selecting V:choose V that minimizes the SER upper bound. The preferred embodimentsfor linear and iterative detectors find the weights V by maximization:V=argmax_(Uεs) min_(1≦m≦M) SINR(m;H,U)where SINR(m; H, U) is the signal-to-interference+noise ratio for themth stream with channel H and weighting matrix U in the set S ofallowable weighting matrices. This criterion corresponds to minimizingthe system bit error rate (BER).

Closed-form expression of SINR(m; H, U) for different detectors can beobtained. Define the following:A=HU (a Q×M matrix)=[a₁,a₂, . . . , a_(M)] (each a_(m) is a Q×1 vector)A_(m)=[a_(m),a_(m+1), . . . , a_(M)] (a Q×(M−m+1) matrix)ThenSINR _(LZF)(m;H,U)=ρ/[A ^(H) A] ⁻¹ _(m,m)SINR(m;H,U)_(LMMSE) =ρ/[I _(M) /ρ+A ^(H) A] ⁻¹ _(m,m)−1SINR _(IZF)(m;H,U)=ρ/[A _(m) ^(H) A _(m)]⁻¹ _(1,1)SINR(m;H,U)_(IMMSE) =ρ/[I _(M) /ρ+A _(m) ^(H) A _(m)]⁻¹ _(1,1)−1And for ordered detection in the iterative detectors, the SINRexpressions are accordingly modified as previously described.

The foregoing gives the criterion to select the optimal weighting matrixV from the pre-determined set of allowable weighting matrices, S_(V).Another aspect of preferred embodiment systems is the selection of thisset S_(V) of allowable weighting matrices. As given above, onepossibility is to choose the following parameterization of V:

$V = \begin{bmatrix}w_{1} & 0 & \cdots & 0 \\0 & w_{2} & \cdots & 0 \\\vdots & \vdots & ⋰ & \vdots \\0 & 0 & \cdots & w_{M}\end{bmatrix}$where each wm belongs to a set of allowable (P/M)×1 vectors S_(wm) asdescribed above. There are several variations: (1) when all w_(m) aredistinct, |S_(V)|=π_(m)|S_(wm)|, so when all S_(wm)=S_(w),|S_(V)|=|S_(w)|^(M); (2) all wm are equal to a single w, and thus|S_(V)|=|S_(w)|.

Note that V can be any P×M linear transformation, so another possibilityis

$V = \begin{bmatrix}R_{1} \\R_{2} \\\vdots \\R_{P/M}\end{bmatrix}$where R_(m) is a M×M unitary rotation matrix. In particular, for M=2:

$R_{m} = \begin{bmatrix}{\cos\;\theta_{m}} & {{\mathbb{e}}^{{j\phi}\; m}\sin\;\theta_{m}} \\{{- {\mathbb{e}}^{{- {j\phi}}\; m}}\sin\;\theta_{m}} & {\cos\;\theta_{m}}\end{bmatrix}$where φ_(m) and φ_(m) can be quantized for low-complexity searching tofind V. See the following simulation section.

5. Simulation Results

FIGS. 4-5 compare raw BER for the P=Q=4 cases of standard MIMO (64 QAMsingle stream space diversity), a double STTD, and various two-streampreferred embodiments (FIG. 2 b) with iterative MMSE detection (withordering) at 4-bps/Hz and 6-bps/Hz throughput. The curves are: (1)DSTTD: open loop with double STTD; (2) Mode1: FIG. 2 d with weightsw₁=½, w_(p)=exp(−jφ_(p)) for p=2, 3, 4 where the φ_(p) are uniformlyquantized to 2 bits, so the allowable weight space size is 4³=64; (3)DTXAA . . . M1: weight matrix of two 2×1 phase vectors w₁ and w₂ witheach phase of 2-bit quantization, so a total weight space size of 16;(4) DTXAA . . . M3: weight matrix of two 2×1 vectors w₁ and w₂ with eachvector of 1-bit magnitude and 2-bit phase quantization, so a totalweight space size of 64; (5) DTXAA . . . Rot N=4: weight matrix (FIG. 2c) is 2×1 of 2×2 blocks with each 2×2 block a rotation by θ_(m) withθ_(m) uniformly quantized in range [0,π/2) to 4 values, so the weightspace size is 16; and (6) DTXAA . . . Rot N=8: weight matrix is 2×1 of2×2 blocks with each 2×2 block a rotation by θ_(m) with θ_(m) uniformlyquantized in range [0,π/2) to 8 values, so the weight space size is 64.Observe that for the same set size, the DTXAA (preferred embodiments)outperforms the conventional by up to 2.5 dB. Even with smaller setsize, the preferred embodiments still outperfoms the conventional by upto 2.2 dB. Note that curve (4) performs the best.

6. Modifications

The preferred embodiments can be modified in various ways whileretaining the features of antenna weightings determined from thecomposite channel.

For example, as mentioned before, other receiver schemes can be used,which result in different error rate or SINR dependence upon the channeland weight vectors. For TDMA and CDMA systems, the channel may exhibitsignificant frequency selectivity due to multipath effect. In this case,the weight selection criterion must incorporate the effect of multipathinterference as well as the receiver scheme that is used to suppressmultipath interference. Finally, this scheme can also be applied inOFDM-type systems, where the scheme is applied for each sub-carrier oracross sub-carriers.

1. A method of transmission of a symbol stream, comprising: (a)providing P transmit antennas where P is an integer greater than orequal to 3; (b) splitting a data stream into M symbol streams totransmit from the P antennas through communication channels where M isan integer greater than or equal to 2; and (c) multiplying the symbolstreams by a rectangular matrix that corresponds to a diagonal M×M blockmatrix of (P/M)×1 vectors where each (P/M)×1 vector corresponds toweights for a symbol stream of the M symbol streams.
 2. The method ofclaim 1 including deriving the weights from estimates of communicationchannels from said P antennas to at least one Q receive antenna where Qis a positive integer.
 3. The method of claim 2 including detecting saidM symbol streams at said Q antenna.
 4. The method of claim 2 includingdetecting the M symbol streams using one of linear zero-forcing, linearminimum mean square error, iterative zero-forcing, and iterative minimummean square error.
 5. The method of claim 2 including detecting the Msymbol streams using a maximum likelihood detector with SER selectioncriterion.
 6. The method of claim 1 including selecting the weights froma finite set of P-by-M matrices.
 7. The method of claim 1 includingselecting the weights by maximizing a minimumsignal-to-interference-plus-noise ratio of said M symbol streams afterdetection.
 8. The method of claim 1 in which the weights correspond to a(P/M)×1 vector matrix of M×M blocks where each M×M block is an M×Munitary matrix.
 9. The method of claim 1 including receiving the weightsfrom a receiver in said channels.
 10. The method of claim 9 includingproviding the weights from channel information in said receiver.
 11. Themethod of claim 1 including: (a) deriving said weights of step (c) fromestimates of communication channels from said P antennas to at least oneQ receive antenna; (b) updating said channel estimates; and (c) updatingsaid weights in response to updating said channel estimates.
 12. Themethod of claim 1 including deriving the M symbol streams from a singleinput symbol stream.
 13. The method of claim 1, wherein at least one ofsaid communication channels is a wideband or code division multipleaccess (CDMA) channel with multiple users.
 14. The method of claim 1,wherein at least one of said communication channels is a wideband orCDMA channel with a single user with multiple codes.
 15. The method ofclaim 1, wherein at least one of said communication channels is anarrowband or time division multiple access (TDMA) channel.
 16. Themethod of claim 1, wherein at least one of said communication channelsis an OFDM-type channel.
 17. The method of claim 1 in which each antennaweight is a vector w_(m) corresponding to a symbol stream, and includingproviding weights in accordance with a weighting matrix V, where:$V\begin{matrix}w_{1} & 0 & \ldots & 0 \\0 & w_{2} & \ldots & 0 \\\vdots & \vdots & \vdots & \vdots \\0 & 0 & \ldots & w_{m}\end{matrix}$ where each vector w_(m) belongs to a set of (P/M)×1vectors.
 18. The method of claim 1 including transmitting from each Ptransmit antenna in user equipment.
 19. The method of claim 1 includingtransmitting from each P transmit antenna in a mobile device.
 20. Themethod of claim 1 including transmitting from each P transmit antenna asymbol stream multiplied by a weight.